#13103308

order	1600
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₄

Aliases

No aliases for this group.

C₅² ⋊ #433

	subgroup	G/H
center, Frattini, hypercenter	C₄	(D₅⋊AGL(1,𝔽₅))⋊C₂
commutator	C₂×C₅⋊D₅	C₂²×C₄
Fitting	C₄×C₅²	#41
socle	C₂×C₅²	#117
prime radical	C₂×D₅²	C₂×C₄
cosocle	C₄×C₅⋊D₅	C₂³
hypocenter	C₅²	#433
LCS	G ▷ C₂×C₅⋊D₅ ▷ C₅²
UCS	C₁ ◁ C₄

176 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 80

Polycyclic presentation:

2^6,5^2|b^2=d,c^2=e,e^2=f,b^a=bf,c^a=cdf,g^a=g^4,c^b=cdf,g^b=g^2,h^b=h^3,g^c=h^4,h^c=g^4,g^d=g^4,h^d=h^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5660);